Solution to exchanges 10.2 puzzle: borrowing in the limit as our nerdiness goes to infinity

This is a solution to the editor's puzzle from issue 10.2 of SIGecom Exchanges [Reeves 2011]. The Puzzle asks to determine a point in time such that a lump sum payment of $S will be equivalent to a continuous stream of infinitesimal payments totaling $S, spread evenly over time. The full puzzle can be found online at: http://www.sigecom.org/exchanges/volume_10/2/puzzle.pdf.